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arXiv · 1701.07536

A homotopy method for solving multilinear systems with M-tensors

Lixing Han
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Abstract

Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive solution to a multilinear system with a nonsingular M-tensor and a positive right side vector. We analyze the method and prove its convergence to the desired solution. We report some numerical results based on an implementation of the proposed method using a prediction-correction approach for path following.

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Lixing Han. 2017-01-26. A homotopy method for solving multilinear systems with M-tensors. https://arxiv.org/abs/1701.07536

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